'Add scene ' in Video Editing doesn't insert the whole scene
You need to set the "End Frame" for the scenes, both the one containing the animation and the scene for the VSE.
The end frame setting can be found in the Render tab under the Dimensions section of the Properties window.
Or in the header of the timeline, here it is simply named "End".

If you have the animation scene's length set right the whole clip will show up in the VSE, but it will only render 200 frames.
However if you only set the VSE scene's length, and leave the other at 200, you will only see 200 frames in the VSE, and it will only render what is in the VSE.